Keywords: uncertainty, fuzzy number, spatial-temporal fuzzy interpolation, fuzzy digital bathymetric model, morphodynamics.

An object-oriented database-supported digital bathymetric model with the associated interpretation rules was previously presented [1]. Spatial-temporal interpolation methods and the optimization of the interpolation algorithms to handle non-homogeneously distributed spatial and temporal measurements were discussed. Different procedures for a more adequate analysis of morphodynamics were tested.

This paper elaborates the uncertainty associated with the digital bathymetric model proposed in [1] and discusses how this uncertainty can be incorporated in the model. The tolerance of the measuring instruments, the spatial and temporal densities of the measured data, the methods used for interpolation and the morphologic and morphodymanic characteristics of the area corresponding to the data set are the sources of uncertainty. These different sources of uncertainty and impreciseness are considered here to build a fuzzy digital bathymetric model.

In this paper a fuzzy digital bathymetric model is introduced. The sources of uncertainty in the process of building a spatial-temporal digital bathymetric model are presented. The construction of fuzzy numbers out of the sources of uncertainty is demonstrated. The different cases of fuzzy interpolation are a subject of discussion. The possible techniques for analysis of morphodynamics and the one adopted here are highlighted. The proposed digital bathymetric model has been implemented and the practicability is shown using bathymetric data sets that cover the offshore area of the island of Langeoog off the German coast of the North Sea. The impreciseness of the depth values, the uncertainty induced by the interpolation method, the density of the data set and the characteristic of the investigated area are used together to build a spatial temporal fuzzy bathymetric model. The interpolation procedure is a fuzzy bilinear interpolation based on the supplied grid. This model serves as a basis for further analysis. The fuzzy erosion and sedimentation rates are identified as an example of the fuzzy analysis of the morphodynamics.

Spatial-temporal fuzzy interpolation and analysis are shown to extend spatial-temporal interpolation to model the morphodynamic processes in a more comprehensive way. They guarantee a complete interpretation of all available information on the measured basic data. For instance, one can derive at any arbitrary point of time a consistent fuzzy digital bathymetric model, with which the deduced uncertainty is quantified at every location. The rates of erosion and sedimentation with their associated uncertainty can then be quantified.

1

P. Milbradt, C. Dorow, "Identification of Morphological Tendencies and Velocities in Coastal Zones", 7th ISE and 8th HIC, Chile, 2009.

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